All the VIP lounges in Rome and Milan are very similar, with nice selections of snacks and coffees. Liquor is free and sometimes there are more substantial meals. The nicest lounges are those inside security... for transit passengers. They have showers and often special areas just for Magnifica Class passengers (not Prima class like intra-Europe business class).

In Rome, there is a single lounge OUTSIDE of security in Terminal A just to the right of the ticket counter when you walk in. As for Milan, I cannot tell from my diagram whether there is a lounge outside of security or not. I would venture a guess that there is: near Satellite A on the middle level.

According to the Diner's Club website, none of the AZ VIP lounges accept Diner's Club members. I do not believe Hertz Gold members have airport lounge access as a privilege. Nonetheless, AZ's generous policy about any C-class passenger getting lounge access makes every lounge quite crowded.